On the Unity of Quantitative Methods of Pricing in Finance and Insurance

A. V. Melnikov

Informatics and Automation, Stochastic financial mathematics, Tome 237 (2002), pp. 57-79.

Résumé

A relationship between the calculation of premiums and reserves in insurance and finance is studied. It is shown how traditional actuarial methods of calculation in property insurance are derived from the financial no-arbitrage principle. A general method is presented for estimating the probability of ruin of an insurance company. In life insurance, the main emphasis is placed on the description of innovation schemes of “flexible” insurance, and it is pointed out that the calculation of the corresponding premiums and reserves is related with the Black–Scholes formula and equation. A new approach to the insurance and reinsurance of catastrophic risks is presented which is based on their diversification on financial markets by means of insurance derivative securities.

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